The Cross Anomalous Dimension in Maximally Supersymmetric Yang--Mills Theory

Abstract

The cross or soft anomalous dimension matrix describes the renormalization of Wilson loops with a self-intersection and is an important object in the study of infrared divergences of scattering amplitudes. In this paper it is studied for the Maldacena--Wilson loop in N=4 supersymmetric Yang--Mills theory and Euclidean kinematics. We consider both the strong-coupling description in terms of minimal surfaces in AdS5 as well as the weak-coupling side up to the two-loop level. In either case, the coefficients of the cross anomalous dimension matrix can be expressed in terms of the cusp anomalous dimension. The strong-coupling description displays a Gross--Ooguri phase transition and we argue that the cross anomalous dimension is an interesting object to study in an integrability-based approach.

arXiv comment30 pages, 8 figures. Version 2: Fixed typos in equations (4.13) - (4.15) and equation (5.28)

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